The present invention relates to a retro-focus type ultra wide angle lens which is well compensated for various aberrations by the use of a non-spherical optical system.
Until now various kinds of retro-focus type wide angle lenses have been known. In the retro-focus type lens system it is desirable to have a sufficiently long back focus, while the compensation of the distortion, the astigmatism or the coma is difficult because of the non-symmetry of the lens system. It is remarkably difficult to compensate for both the distortion and the astigmatism at the same time. Consequently, the larger the field of view is, the higher the number of the lenses is increased in order to compensate various aberrations.
It is well known to introduce a non-spherical surface in order to compensate distortion without complicating the lens system. Because the non-spherical surface influences other aberrations, however, care should be taken in designing the non-spherical surface. In order to compensate the distortion well it is desirable that the non-spherical surface is provided at the position in the lens system at which the distance between the optical axis and the off-axial principal ray with the maximum field of view is as large as possible.
The reason is as follows. Hereby, let .nu. represent the number of respective lens surfaces, h.nu. the height of the position on the .nu.th surface at which the on-axial (paraxial) ray crosses the surface, h.nu. the height of the position on the .nu.th surface at which the principal ray (a ray from the object point to the center of the diaphragm) crosses the surface.
I (Spherical aberration with the third grade aberration coefficient)=.SIGMA.I.nu., PA1 II (Coma)=.SIGMA.II.nu., PA1 III (Astigmatism)=.SIGMA.III.nu., PA1 V (Distortion)=.SIGMA.V.nu.
The amount which the non-spherical element contributes to respective aberration is proportional to h.sup.4 .nu. with reference to I.nu., to h.sup.3 .nu.h.nu. with reference to II.nu., to h.sup.2 .nu.h.nu..sup.2 with reference to III.nu. and to h.nu.h.nu..sup.3 (h.nu.h.nu..sup.5 in fifth order distortions) with reference to V.nu..
As is understood from the above, the surface with large h.nu. but small h.nu. should be formed non-spherically in order to compensate the distortion V by using a non-spherical surface, keeping the influence or other aberrations as small as possible.
Further, even in the range of the higher orders than the fifth, the distortion is proportional to the height h.nu., so that it is effective to form the surface with the large h.nu. non-spherical in order to compensate the distortion.
An example of a retro-focus type wide angle lens in which the distortion is compensated with a non-spherical surface while the astigmatism to be increased as the result is suppressed is disclosed in the U.S. Pat. No. 3,832,035. In case of this example any optical surface in the front divergent lens system is made non-spherical in order to eliminate the distortion, while the astigmatism is compensated by limiting the sum of the thickness at the center of a determined number of lenses.
However, generally in case of the retro-focus type wide angle lenses, as is explained above, the larger the field is, the greater the number of the lenses is increased in order to compensate for various aberrations so that the realization of a compact wide angle lens is desired, for which conventionally no particular consideration has been paid.
When a lens having a non-spherical surface is used in a lens system, more labor and time are required for grinding the lens surface to a non-spherical form than for grinding the lens to a spherical form and thus the manufacturing cost of the lens system will be very high. However, if the lens having a non-spherical surface is made of plastic, the manufacturing cost will be markedly lowered, because the plastic lens can be formed by molds and only several accurate molds make possible a mass production in a short period of time.
However, a plastic lens has the following two defects. First, plastic shows a larger degree of thermal expansion and contraction than glass, and changes in the thickness of the plastic lens produce adverse effects on the total focal length and the back focus of the whole lens system. Secondly, the plastic lens made by molding has a poor surface accuracy as compared with a glass lens. This induces deterioration of the aberration.
A lens system using a plastic lens having a non-spherical surface is disclosed in British Pat. No. 1,388,723, but it has been impossible to provide a high-performance lens system using a plastic lens due to the above-mentioned defects.